Quasi-Topological Cosmology from Emergence of Cosmic Space

We show that one can always derive the Friedmann equation of an (n+1)-dimensional Friedmann–Robertson–Walker universe in cubic quasi-topological gravity, by determining the difference between the bulk and the apparent horizon degrees of freedom in a region of space. We also generalize the study to the higher-order quasi-topological gravity, and extract the corresponding Friedmann equation in this theory by using the same approach.